Hello!
To find the inverse of a function, you switch the x and y variables and solve for y. Here are some characteristics of inverse functions: the domain of f(x) is equal to the range of f^-1(x), and the range of f(x) is equal to the domain of f^-1(x). If f(x) and f^-1(x) are inverses of each other, then they are reflected over the line y = x.
y = -10x + 2 → x = -10y + 2
x = -10y + 2 (subtract 2 from both sides)
x - 2 = -10y (divide both sides by -10)
(x - 2)/-10 = y (simplify)
y = -x/10 + 1/5
Therefore, if f(x) = -10x + 2, then f^-1(x) = -x/10 + 1/5.
